Cholesterol is very important to the cell membrane and makes up about half of the cell membrane while constituting to about 20 percent of the total mass of the membrane.
Cholesterol has a great role in maintaining the fluidity of the cell membrane. It protects the membrane from becoming too fluid and thus helps maintaining its integrity. Cholesterol, like the phospholipids of cell membrane, is amphipathic in nature. ie., it has a polar part and a non-polar part. The polar hydrophilic part of it aligns with the phosphate heads of the membrane phospholipids while its hydrophobic non-polar regions are tucked into the interior of the phospholipid bilayer. This helps in slightly immobilising the outer surface of the membrane, preventing it from being overly fluid.
Cholesterol aids in the fluidity of the membrane too. It is present in high concentrations in the membrane and this has the effect of separating the phospholipids. Thus the fatty acid chains do not come together and crystallize.
Cholesterol also helps in securing membrane proteins within the plasma membrane. It makes an environment in the plasma membrane that makes the membrane impermeable to small water-soluble molecules.
If you add cholesterol to a cell membrane, it will reduce fluidity of the phospholipid membrane. The cholesterol plays an important role because without it the cell would not have that rigidity and support that it needs. The membrane would also be much more permeable allowing molecules we don't want passing through the membrane.